Create scaled_subtraction.py

scaled_subtraction.py

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+import numpy as np
+from scipy.optimize import curve_fit
+from matplotlib import pyplot as plt
+
+def normalize(v):
+    """
+    A helper function to normalize a vector. That is, the sum of the square of each component
+    equals 1.
+    v: A vector to be normalized.
+    Returns: The normalized version of the vector.
+    Throws an exception if the norm is 0.
+    """
+    norm = np.linalg.norm(v)
+    if norm == 0:
+        raise Exception("Function can not take a zero vector!")
+    return (v/norm)
+
+def create_fitting_func(v1, v2):
+    """
+    Use this to generate the function to be fitted.
+    v1: The first basis vector. In our example, the pure plastic vector.
+    v2: The second basis vector. In our example, the pure sugar vector.
+    Returns: A function that takes an x value, and two constants which vary with fitting.
+    """
+    assert(len(v1) == len(v2))
+
+    def func(x, a, b):
+        return (a*v1[x] + b*v2[x])
+    return func
+
+
+def calc_scaled_coeff(measured, spectra_one, spectra_two):
+    """
+    Another helper function. This does the actual work in fitting the data to the model.
+    measured: The measured ydata.
+    spectra_one: The first basis vector, probably plastic.
+    spectra_two: The second basis vector, probably plastic.
+    Returns a tuple of the constants calculated.
+    """
+    xdata = np.arange(len(measured))
+    assert(len(xdata) == len(spectra_one) and len(xdata) == len(spectra_two))
+    y_func = create_fitting_func(spectra_one, spectra_two)
+    popt, pcov = curve_fit(y_func, xdata, measured)
+    return popt
+
+def scaled_subtraction(measured, spectra_one, spectra_two):
+    """
+    The actual scaled_subtraction function intended to be called by other code.
+    measured: The measured ydata.
+    spectra_one: The first basis vector, probably plastic.
+    spectra_two: The second basis vector, probably plastic.
+    Returns a tuple of the two calculated vectors. The order of the vectors corrosponds to the order
+    that the arguments are given. So if the order is plastic and then sugar, you'll get calculated
+    plastic and then calculated sugar.
+    """
+    spectra_one /= np.linalg.norm(spectra_one)
+    spectra_two /= np.linalg.norm(spectra_two)
+    coeffs = calc_scaled_coeff(measured, spectra_one, spectra_two)
+    loading_one = (measured - coeffs[1]*spectra_two)
+    loading_two = (measured - coeffs[0]*spectra_one)
+    return (loading_one, loading_two)